Non-Supersymmetric Attractors in $R^2$ Gravities

TL;DR

This paper explores the attractor mechanism for extremal black holes within general $R^2$ gravity theories, demonstrating the existence of attractor solutions and analyzing the effects of higher derivative interactions and Gauss-Bonnet terms.

Contribution

It provides a detailed analysis of non-supersymmetric attractors in $R^2$ gravities, including the impact of higher derivative terms and moduli coupling, extending previous understanding beyond supersymmetric cases.

Findings

Attractor solutions exist in general $R^2$ gravity theories.

Regularity of moduli fields at the horizon ensures attractor behavior.

The effective potential's extremization determines the attractor point.

Abstract

We investigate the attractor mechanism for spherically symmetric extremal black holes in a theory of general $R^2$ gravity in 4-dimensions, coupled to gauge fields and moduli fields. For the general $R^2$ theory, we look for solutions which are analytic near the horizon, show that they exist and enjoy the attractor behavior. The attractor point is determined by extremization of an effective potential at the horizon. This analysis includes the backreaction and supports the validity of non-supersymmetric attractors in the presence of higher derivative interactions. To include a wider class of solutions, we continue our analysis for the specific case of a Gauss-Bonnet theory which is non-topological, due to the coupling of Gauss-Bonnet terms to the moduli fields. We find that the regularity of moduli fields at the horizon is sufficient for attractor behavior. For the non-analytic sector, this regularity condition in turns implies the minimality of the effective potential at the attractor point.